Solve.
-Determine the area of a circular enclosure and a square enclosure made with 1495 yards of fence. Use $\pi = 3.1416 .$
A) Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $558,756 \mathrm { yd } ^ { 2 }$
B) Circular: $177,857 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$
C) Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$
D) $\text { Circular: } 177,857 \mathrm{yd}^{2} \text {; square: } 558,756 \mathrm{yd}^{2}$

Question

Solve.
-Determine the area of a circular enclosure and a square enclosure made with 1495 yards of fence. Use $\pi = 3.1416 .$ 
A) Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $558,756 \mathrm { yd } ^ { 2 }$
B) Circular: $177,857 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$
C) Circular: $121,244 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$
D) $\text { Circular: } 177,857 \mathrm{yd}^{2} \text {; square: } 558,756 \mathrm{yd}^{2}$

Quizplus · Accepted Answer

For the circular enclosure, the total length of the fence is the circumference of the circle. The formula for the circumference is $C = 2\pi r$, where $r$ is the radius. Given $C = 1495$ yards and $\pi = 3.1416$, we solve for $r$ and then find the area $A = \pi r^2$.$$1495 = 2 \times 3.1416 \times r$$$$r = \frac{1495}{2 \times 3.1416} \approx 238.08 \text{ yards}$$$$A = 3.1416 \times (238.08)^2 \approx 177,857 \text{ square yards}$$For the square enclosure, the total length of the fence is the perimeter of the square. The formula for the perimeter of a square is $P = 4s$, where $s$ is the length of one side. Given $P = 1495$ yards, we solve for $s$ and then find the area $A = s^2$.$$1495 = 4s$$$$s = \frac{1495}{4} = 373.75 \text{ yards}$$$$A = (373.75)^2 = 139,689 \text{ square yards}$$Therefore, the correct answer is B) Circular: $177,857 \mathrm { yd } ^ { 2 }$; square: $139,689 \mathrm { yd } ^ { 2 }$.

Solve -Determine the Area of a Circular Enclosure and a Square

Solve
-Determine the Area of a Circular Enclosure and a Square